**Knowledge Graph Convolutional Network (KGCN)**

Knowledge graphs capture interlinked information between entities and they represent an attractive source of structured information that can be harnessed for recommender systems. However, existing recommender engines use knowledge graphs by manually designing features, do not allow for end-to-end training, or provide poor scalability. Here we propose Knowledge Graph Convolutional Networks (KGCN), an end-to-end trainable framework that harnesses item relationships captured by the knowledge graph to provide better recommendations. Conceptually, KGCN computes user-specific item embeddings by first applying a trainable function that identifies important knowledge graph relations for a given user and then transforming the knowledge graph into a user-specific weighted graph. Then, KGCN applies a graph convolutional neural network that computes an embedding of an item node by propagating and aggregating knowledge graph neighborhood information. Moreover, to provide better inductive bias KGCN uses label smoothness (LS), which provides regularization over edge weights and we prove that it is equivalent to label propagation scheme on a graph. Finally, We unify KGCN and LS regularization, and present a scalable minibatch implementation for KGCN-LS model. Experiments show that KGCN-LS outperforms strong baselines in four datasets. KGCN-LS also achieves great performance in sparse scenarios and is highly scalable with respect to the knowledge graph size. … **Temporal Causal Model**

Temporal causal modeling attempts to discover key causal relationships in time series data. In temporal causal modeling, you specify a set of target series anda set of candidate inputs to those targets. The procedure then builds an autoregressivetime series model for each target and includes only those inputs that have a causalrelationship with the target. This approach differs from traditional time series modelingwhere you must explicitly specify the predictors for a target series. Since temporalcausal modeling typically involves building models for multiple related time series, theresult is referred to as a model system. In the context of temporal causal modeling, the term causal refers to Granger causality. A time series X is said to ‘Grangercause’ another time series Y if regressing for Y in terms of past values of both X and Yresults in a better model for Y than regressing only on past values of Y. … **Differential Temporal Difference Learning**

Value functions derived from Markov decision processes arise as a central component of algorithms as well as performance metrics in many statistics and engineering applications of machine learning techniques. Computation of the solution to the associated Bellman equations is challenging in most practical cases of interest. A popular class of approximation techniques, known as Temporal Difference (TD) learning algorithms, are an important sub-class of general reinforcement learning methods. The algorithms introduced in this paper are intended to resolve two well-known difficulties of TD-learning approaches: Their slow convergence due to very high variance, and the fact that, for the problem of computing the relative value function, consistent algorithms exist only in special cases. First we show that the gradients of these value functions admit a representation that lends itself to algorithm design. Based on this result, a new class of differential TD-learning algorithms is introduced. For Markovian models on Euclidean space with smooth dynamics, the algorithms are shown to be consistent under general conditions. Numerical results show dramatic variance reduction when compared to standard methods. … **Mixture Model (MM)**

In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with “mixture distributions” relate to deriving the properties of the overall population from those of the sub-populations, “mixture models” are used to make statistical inferences about the properties of the sub-populations given only observations on the pooled population, without sub-population identity information. …

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